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MMO 354 Moscow MO 1957 equal segments lead to parallel sides

Source:

August 20, 2019
geometrymidpointsparallelequal segments

Problem Statement

In a quadrilateral ABCDABCD points MM and NN are the midpoints of the diagonals ACAC and BDBD, respectively. The line through MM and NN meets ABAB and CDCD at M′M' and N′N', respectively. Prove that if MM′=NN′MM' = NN', then AD//BCAD // BC.
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